Build the Linear Regression

Here we will learn how to find the intercept and slope for our dataset. For this example, we will use a scientific computation library SciPy, to import stats. Using the method stats.lingress() we can get the most important linear regression parameters for the given dataset (x and y arrays). Pay attention to the first two values (slope and intercept), and other parameters will be analyzed in the following chapters. These two numbers define a straight line. The squares of the residuals of the dataset to points are minimal.

# Import the libraries

import matplotlib.pyplot as plt

from scipy import stats

# Initialize the data

x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7]

y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7]

# Get the linear regression parameters

slope, intercept, r, p, std_err = stats.linregress(x, y)

# The line shows the dependence of the height of cats on their weight

def on_weight(x):

return slope * x + intercept

# Define the line

height_on_weight = list(map(on_weight, x))

# Add titles to axes

ax = plt.gca()

ax.set_xlabel('Cat height (inches)')

ax.set_ylabel('Cat weight (kg)')

# Visualize our data

plt.scatter(x, y)

plt.plot(x, height_on_weight)

plt.show()


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# Import the libraries
import matplotlib.pyplot as plt
from scipy import stats 

# Initialize the data
x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7] 
y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7] 

# Get the linear regression parameters 
slope, intercept, r, p, std_err = stats.linregress(x, y) 

# The line shows the dependence of the height of cats on their weight 
def on_weight(x): 
   return slope * x + intercept 

# Define the line 
height_on_weight = list(map(on_weight, x)) 

# Add titles to axes 
ax = plt.gca()
ax.set_xlabel('Cat height (inches)')
ax.set_ylabel('Cat weight (kg)') 

# Visualize our data 
plt.scatter(x, y) 
plt.plot(x, height_on_weight) 
plt.show()

The output of the code execution is identical to your first task. However, now we don't work with predefined values but with a method that returns them to us knowing the dataset.

Tarefa

Swipe to start coding

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

[Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
[Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
[Lines #26-27] Build line on your plot.

Solução

# Import the libraries

import matplotlib.pyplot as plt

from scipy import stats

# Initialize the data

x = [1.8, 2.24, 11.2, 7, 4.2, 9.3, 10.3, 6.3, 1.4, 5.8, 1.1, 4.3]

y = [111, 130, 450, 320, 195, 360, 402, 272, 85, 263, 105, 237]

# Get the linear regression parameters

slope, intercept, r, p, std_err = stats.linregress(x, y)

# The line shows the dependence of the number of calories on cats' weight

def on_weight(x):

return slope * x + intercept

# Define the line

feed_on_weight = list(map(on_weight, x))

# Add titles to axes

ax = plt.gca()

ax.set_xlabel('Cat weight (kg)')

ax.set_ylabel('Cat ration (calories)')

# Visualize our data

plt.scatter(x, y)

plt.plot(x, feed_on_weight)

plt.show()

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Seção 1. Capítulo 3

# Import the libraries

import matplotlib.pyplot as ___

from ___ import ___

# Initialize the data

x = [1.8, 2.24, 11.2, 7, 4.2, 9.3, 10.3, 6.3, 1.4, 5.8, 1.1, 4.3]

y = [111, 130, 450, 320, 195, 360, 402, 272, 85, 263, 105, 237]

# Get the linear regression parameters

slope, intercept, r, p, std_err = stats.___(x, y)

# The line shows the dependence of the number of calories on cats' weight

def on_weight(x):

return slope * ___ + intercept

# Define the line

feed_on_weight = list(map(___, x))

# Add titles to axes

ax = plt.gca()

ax.set_xlabel('Cat weight (kg)')

ax.set_ylabel('Cat ration (calories)')

# Visualize our data

plt.scatter(x, y)

plt.___(x, feed_on_weight)

plt.___()

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